Method and apparatus for enhanced multiple coil imaging

ABSTRACT

The subject invention pertains to a method and apparatus for enhanced multiple coil imaging. The subject invention is advantageous for use in imaging devices, such as MRIs where multiple images can be combined to form a single composite image. In one specific embodiment, the subject method and apparatus utilize a novel process of converting from the original signal vector in the time domain to allow the subject invention to be installed in-line with current MRI devices.

CROSS-REFERENCE TO RELATED APPLICATION

[0001] The present application claims the benefit of U.S. ProvisionalApplication No. 60/299,012, filed Jun. 18, 2001, which is herebyincorporated by reference herein in its entirety, including any figures,tables, or drawings.

[0002] The subject invention was made with government support under aresearch project supported by the National Institutes of Health (NIH),Department of Health and Human Services, Grant Number 5R44 RR11034-03.The government has certain rights in this invention.

BACKGROUND OF THE INVENTION

[0003] The subject invention relates to the field of medical technologyand can provide for an improved method of creating composite images froma plurality of individual signals. The subject invention is particularlyadvantageous in the field of magnetic resonance imaging (MRI) where manyindividual images can be used to create a single composite image.

[0004] In the early stages of MRI development, typical MRI systemsutilized a single receiver channel and radio frequency (RF) coil. Inorder to improve performance, multi-coil systems employing multiple RFcoils and receivers can now be utilized. During operation of thesemulti-receiver systems, each receiver can be used to produce anindividual image of the subject such that if there is n receivers therewill be n images. The n images can then be processed to produce a singlecomposite image.

[0005] Many current systems incorporate a sum-of-squares (SOS)algorithm, where the value of each pixel in the composite image is thesquare-root of the sum of the squares of the corresponding values of thepixels from each of the n individual images. Where the pixel values arecomplex, the value of each pixel in the composite image is thesquare-root of the sum of the magnitude squared of the correspondingpixels from each of the individual images. In mathematical terms, if ncoils produce n signals s=(s₁, s₂, s₃, . . . , s_(n)) corresponding tothe pixel values from a given location, the composite signal pixel isgiven by the following equation:

{square root}{square root over (S ^(t) ·S)}

[0006] Some systems also incorporate measurement and use of the noisevariances of each coil. Each of the n individual channel gains can thenbe adjusted after acquisition to produce equal noise variance individualimages. Following this procedure, the SOS algorithm can then be applied.This additional procedure tends to improve the signal-to-noise ratio(SNR) of the process but may still fail to optimize the SNR of theresultant composite image. This results in an equation:

{square root}{square root over (S ^(t) ·[Diag(N)]⁻¹ ·S)}

[0007] It can be shown that the SOS algorithm is optimal if the noisecovariance matrix is the identity matrix. In order to further optimizethe SNR of the resultant composite image, it would be helpful to haveknowledge of the noise covariance matrix. Optimal SNR reconstruction inthe presence of noise covariance can be summarized by the followingsimple equation:

{square root}{square root over (S ^(t) ·[N] ⁻¹ ·S)}

[0008] U.S. Pat. Nos. 4,885,541 and 4,946,121 discuss algorithmsrelating to equations which are similar in form. Typically this methodis applied in the image domain, after acquisition and Fouriertransformation into separate images.

BRIEF SUMMARY OF THE INVENTION

[0009] The subject invention pertains to a method and apparatus forimproved processing of electrical signals. A specific embodiment of thesubject invention can be used with MRI devices. The subject method andapparatus can be used to combine a plurality of individual images into asingle composite image. The composite image can have reduced distortionand/or increased signal to noise ratio. In one embodiment, the subjectmethod and apparatus can be installed as an aftermarket addition toexisting MRI devices in order to take advantages of the method hereindescribed. In another embodiment, the subject invention can beincorporated into new MRI devices and/or systems.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010]FIG. 1 shows a schematic representation of a specific embodimentof the subject invention.

[0011]FIG. 2 shows a schematic representation of a specific embodimentof the subject invention.

[0012]FIG. 3 shows a clinical image superimposed with percent gains ofthe optimal SNR with respect to the embodiments shown in FIG. 2 pverstandard SOS SNR.

[0013]FIG. 4A shows a flowchart for standard SOS processing.

[0014]FIG. 4B shows a flowchart for a specific embodiment of the subjectinvention.

[0015]FIG. 4C shows a flowchart for a specific embodiment of the subjectinvention.

[0016]FIG. 4D shows a flowchart for a specific embodiment of the subjectinvention.

DETAILED DESCRIPTION OF THE INVENTION

[0017] The subject invention pertains to a method and apparatus forenhanced multiple coil imaging. The subject invention is advantageousfor use in imaging devices, such as MRIs where multiple images can becombined to form a single composite image. In one specific embodiment,the subject method and apparatus utilize a novel process of convertingfrom the original signal vector in the time domain to allow the subjectinvention to be installed in-line with current MRI devices.

[0018] An MRI device, which could be used with the subject invention,typically has multiple RF coils and receivers where each coil canproduce an image of the subject. Thus, a preferred first step in the useof a multi-receiver MRI system is to produce n data sets which could beused to produce n images, one from each of the n receivers employed bythe device. In typical MRI devices, a next step can be to produce asingle composite image using the n individual images. This compositeimaging is commonly formed through the manipulation of the n individualimages in a sum-of-squares (SOS) algorithm. In this process, the valueof each pixel in the composite image is the sum of the squares of thecorresponding values of the pixels from each of the n individual images.Where the pixel values are complex, the sum of the value of each pixelin the composite image is the sum of the magnitude squared of thecorresponding pixels from each of the individual images. In mathematicalterms, if n coils produce n signals s=(s₁, s₂, s₃, . . . , s_(n))corresponding to the pixel values from a given location, the compositesignal pixel is given by the following equation:

{square root}{square root over (S ^(t) ·S)}

[0019] Some systems also incorporate measurement and use of the noisevariances of each coil. Each of the n individual channel gains can thenbe adjusted after acquisition to produce equal noise variance individualimages. Following this procedure, the SOS algorithm can then be applied.This additional procedure tends to improve the signal-to-noise ratio(SNR) of the process but may still fail to optimize the SNR of theresultant composite image. This results in an equation:

{square root}{square root over (S ^(t) ·[Diag(N)]⁻¹ ·S)}

[0020] It can be shown that the SOS algorithm is optimal if noisecovariance matrix is the identity matrix. In order to further optimizethe SNR of the resultant composite image, it would be helpful to haveknowledge of the relative receiver profiles of all the coils andknowledge of the noise covariance matrix. For illustrative purposes, thenoise covariance matrix can be referred to as N, a n×n Hermitiansymmetric matrix. One can also consider optimal given no a prioriknowledge (i.e. no information about the coil receive profiles). Optimalthen considers only the knowledge of the noise covariance matrix andassumes that the relative pixel value at each location is approximatelythe relative reception ability of each coil. It can be shown that theSOS algorithm is optimal if the noise covariance matrix is the identitymatrix. This method can be summarized by the following simple equation:

{square root}{square root over (S ^(t) ·[N] ⁻¹ ·S)}

[0021] U.S. Pat. Nos. 4,885,541 and 4,946,121, which are herebyincorporated herein by reference, discuss algorithms relating toequations which are similar in form. Typically this method is applied inthe image domain, after acquisition and Fourier transformation intoseparate images. In order to further optimize the SNR of the resultantcomposite image, it would be helpful to have knowledge of the relativereceiver profiles of all the coils and knowledge of the noise covariancematrix. As the matrix N⁻¹ is Hermitian symmetric, N⁻¹ can therefore beexpressed in an alternate form as N=K^(t)K.

[0022] This allows the equation above to be rewritten as:

{square root}{square root over (s ^(t) ·[K ^(t) K] ⁻¹ ·s)}={squareroot}{square root over (s ^(t) ·K ⁻¹ K ^(t) ⁻¹ ·s)}={square root}{squareroot over ((K ^(t) ⁻¹ s)^(t) ·K ^(t) ⁻¹ s)}

[0023] This is now in the form:

{square root}{square root over (Ŝ)} ^(t) ·Ŝ

[0024] Therefore, it is as if the conventional SOS algorithm isperformed on a new vector, Ŝ. Viewed another way, this optimal equationis equivalent to a Sum of Squares operation after a basis transformationto an uncorrelated basis. The new basis can be considered channels thatare noise eigenmodes of the original coil. In a specific embodiment ofthe subject invention, the process of converting from the originalsignal vector to a new signal vector can be a linear processcorresponding to, for example, multiplication by constant values andaddition of vector elements. When only multiplication by constant valuesand addition of vector elements are used, the process can occur beforeor after Fourier Transformation. That is, the process can occur in thetime domain or in the image domain.

[0025] Accordingly, the subject method and apparatus can operate in thetime domain to convert an original signal vector, which is typically ina correlated noise basis, to a new signal vector, which can be in anuncorrelated noise basis. In a specific embodiment of the subjectinvention, standard reconstruction algorithms for producing compositeimages can be used. These algorithms are already in place on manymulti-channel MRI systems. In addition, it may be possible to applyother algorithms for spatial encoding such as SMASH and SENSE withbetter efficiency.

[0026] In a specific embodiment, the subject method and apparatus canincorporate the processing of each signal with the coil so that theprocessing does not show to a user, such as to create the effect of“pseudo coils” having 0 noise covariance. The subject invention can beimplemented via software and/or hardware.

[0027]FIG. 1 shows a schematic representation of a specific embodimentof the subject invention. This embodiment can be placed afterpreamplification and can also be placed within a specific coil package.The device parameters can be gathered from average noise covariance dataobtained, for example, from tests on typical subjects. Alternatively,the noise parameters can be obtained internal to the device using noisecorrelators whose outputs could be used to set gains or attenuations toproduce the desired result. Alternative embodiments can be placed beforepreamplifications.

[0028] The subject method can allow for a reduction in the number ofchannels and, in a specific embodiment, be generalized to an optimalreduction in the number of channels. In some embodiments, a coil arraycan have some degree of symmetry. With respect to coil arrays havingsome degree of symmetry, there can exist eigenvalues with degenerateeigenvectors. Generally, two eigenvectors with the same (or similar)eigenvalue can represent similar effective imaging profiles, oftenhaving some shift or rotation in the patterns. Accordingly, channelswith the same eigenvalues can be added with some particular phase,resulting in little loss in SNR and partially parallel acquisition (PPA)capability. This can allow for maximizing the information content perchannel. In a specific embodiment, adding the signals from channels withidentical (or similar) eigenvalues, the number of channels may bereduced from n to m, where m<n, channels with little loss inperformance. In a specific embodiment, such a reduction in the number ofchannels can be implemented with respect to quadrature volume coilchannels. For example, if two volume coils or modes have fields whichare uniform and perpendicular, then the circularly polarized addition ofthese fields, for example by adding the fields 90 degrees out of phase,can allow all of the signal into one channel and no signal into theother channel. In this example, the use of a phased addition associatedwith the uniform modes both having the same eigenvalves and beingrelated through a rotation of 90 degrees allows the conversion of twocoils to one channel to be accomplished.

[0029] Referring to FIGS. 4A-4B, a comparison of the standard method forproducing a single composite image from the output signals of N coils toan embodiment of the subject invention which incorporates a decorrelatorinto which N signals are inputted and M signals are outputted, whereM≦N. such that a single composite image is produced from the M outputtedsignals after processing. FIGS. 4C and 4D show flowcharts for otherembodiments of the subject invention. FIG. 4A shows a flowchart for thestandard method of producing a single composite image from the outputsignals of N coils in a MRI system. The N signals are preamplified andthen mixed to lower frequencies. The N lower frequency signals are thensampled by A/D converters to produce N digital signals. 2D FourierTransforms are applied to the N digital signals followed bymultiplication by N image domain matrices to produce a single compositeimage. FIG. 4B shows a flowchart for a specific embodiment of thesubject invention similar to the standard method of FIG. 4A with the Nsignals outputted from the preamplifier inputted to a decorrelator whichoutputs M signals, where M≦N. Accordingly, the remaining processingshown in FIG. 4B is for M signals, rather than N. FIG. 4C shows aflowchart for another specific embodiment of the subject invention whichcan implement the “optimal” reconstruction utilizing a softwareimplementation. In this embodiment, the software implementing theoptimal reconstruction is based on the previously measured noisecovariance matrix U, such that processing of the N signals outputtedafter processing by the N image domain matrices produces the outputimage. FIG. 4D shows the flowchart for another specific embodiment inaccordance with the subject invention where, after preamplification andoptional additional amplification, the N signals from the N coilsundergo direct digitization and are inputted to a DSP for 2D FourierTransform and matrix operations using the K matrix, where N is the noisecovariance matrix and N=K^(t)K to produce an output image. This approachwould be a more efficient algorithm than prior art would provide.

EXAMPLE 1

[0030] This example describes a 4-channel hardware RF combiner networkwhich realizes a basis change to reduced noise correlation. The RFcombiner network can realize a basis change to minimal noisecorrelation. Such a basis change to minimal noise correlation canoptimize SNR achievable using the Sum-of-Squares reconstruction method.The network can be realized using passive RF components. A specificembodiment was tested specifically using a 4-channel head coil on a 1.5Tscanner. SNR gains of over 30% can be achieved in the periphery, withcorresponding loss in uniformity. Noise correlation can be greatlyreduced when using the combiner. Results from the measurements agreeclosely with software techniques.

[0031] A head coil design has demonstrated greater than 20% peripheralSNR gain by using “optimal” reconstruction offline from raw data.“Optimal” can be defined as reconstructing with the highest SNR usingthe signal plus noise as an estimate of the true signal, but with thefull noise covariance matrix taken into account. The standardSum-of-Squares reconstruction can be optimized for SNR by employing thenoise correlation matrix. However, there are practicality issues and canbe a lack of any substantial gain in image quality (i.e. 10% or less).The Sum of Squares (with normalized variances) can be optimal of thenoise covariance matrix is diagonal (no correlation between channels).To achieve this gain in clinical practice, a hardware combiner circuithas been developed to achieve this SNR gain for a specific coil on atypical MRI scanner without software modification.

[0032] The standard Sum-of-Squares (SoS) reconstruction from ann-channel array for each pixel is S_(SOS)=s′s where s=(s₁ . . . s_(n)).The optimal reconstruction using only signal data is S_(opt)=s′N⁻¹swhere N is the noise correlation matrix. To yield this optimal resultfrom a standard SoS operation, a signal basis change can be employed.Since in general N′=N, there exists a K constructed viaeigenvalue/vector decomposition such that N=K′K and soS_(opt)=s′K⁻¹K′⁻¹s. Thus we can define ŝ=K′⁻¹s as our new signal vectorand S_(opt)=ŝ′ŝ which is just a SoS operation.

[0033] In hardware, multiplication of the 4 element signal vector s by amatrix is equivalent to using a 4-in-to-4-out network which in generalis complicated by phase shifts and gain scaling, and must almostcertainly be placed after preamplification. The 4-channel head coil usedin this example has 4 sets of opposing parallel-combined loops and wasdescribed in King, S. B. et al. 9^(th) ISMRM proceedings, p. 1090, 2001,which is incorporated herein by reference. Its symmetry yields anall-real noise correlation matrix and corresponding signal basis changematrix of the form shown below: $N = {{\begin{matrix}1 & {.5} & {.5} & {.1} \\{.5} & 1 & {.1} & {- {.5}} \\{.5} & {.5} & 1 & {.5} \\{.5} & {- {.5}} & {.5} & 1\end{matrix}\quad K^{i - t}} = \begin{matrix}{- {.7}} & 1 & 0 & {.7} \\{.7} & 1 & 0 & {- {.7}} \\{.7} & 0 & 1 & {.7} \\{.7} & 0 & {- 1} & {.7}\end{matrix}}$

[0034] The basis change matrix diagonalizes N, so in the new basis thereis no noise correlation, which maximizes SNR.

[0035] The ±0.7 entries in K are just 3 dB attenuations, resulting inthe very simple circuit realization of FIG. 2. Each 4-way splitteroutput is 3dB lower than each 2-way output so no additional attenuationsare needed. The −1 polarity inversions are realized using baluns. Allcomponents are standard RF parts which utilize ferrite cores, so thecircuit was kept far out of the bore.

[0036] Images were made using a 1.5T scanner. FIG. 3 shows a clinicalimage superimposed with percent gains of the hardware-optimal SNR overregular SoS SNR. The combiner circuit was easily inserted and removedwithout disturbing the coil to enable accurate comparisons.

[0037] Clearly the SNR gain is mainly in the periphery and the resultingimage suffers in uniformity between the center and the periphery.Hardware results are also in close agreement with software-optimalreconstruction using normal coil data. Noise correlation issignificantly decreased when using the hardware-optimal combiner, andthe matrix is nearly diagonal as expected: Noise Correlation MatricesNormal Coil w Hardware Combiner 1.00 0.50 0.40 0.11 1.00 0.05 0.12 0.050.50 1.00 0.10 0.57 0.05 1.00 0.07 0.15 0.40 0.10 1.00 0.48 0.12 0.071.00 0.10 0.11 0.57 0.48 1.00 0.05 0.15 0.10 1.00

[0038] The results of this example illustrate that a hardwareDe-correlator can be used to approximate “optimal” reconstruction usingsoftware sums of squares algorithm. As the symmetry of noise covarianceentries is more important than particular values, this device can showrobustness across different loading conditions.

[0039] SENSE and SMASH reconstruction algorithms use the noisecorrelation routinely, so the use of a hardware combiner solely toachieve better SNR is limited. However, this and similar combiners mayfind use in reducing computational time and improving numericalstability in the various new reconstruction algorithms being developed.

[0040] It should be understood that the examples and embodimentsdescribed herein are for illustrative purposes only and that variousmodifications or changes in light thereof will be suggested to personsskilled in the art and are to be included within the spirit and purviewof this application and the scope of the appended claims.

We claim:
 1. A method of processing magnetic resonance imaging signalsfrom a plurality of magnetic resonance imaging coils,comprising:determining a noise covariance matrix, N, of a plurality ofmagnetic resonance imaging coils; receiving a corresponding plurality ofsignals, s=(s₁, s₂, s₃, . . . , s_(n)) from the plurality of coils,wherein the plurality of signals represent a corresponding plurality ofpixel values for a location; calculating a composite pixel value for thelocation, {square root}{square root over (Ŝ)}^(t)·Ŝ where Ŝ^(t)=(K^(t)⁻¹ s)^(t), Ŝ=(K^(t) ⁻¹ s) and N=K^(t)K.
 2. The method according to claim1, wherein the noise covariance matrix, N, of the plurality of magneticresonance imaging coils is a Hermitian symmetric matrix.
 3. The methodaccording to claim 1, wherein (ŝ=ŝ₁, ŝ₂, . . . , ŝ_(n)) is produced byinputting s=(s₁, s₂, . . . , s_(n)) into a circuit, wherein the outputof the circuit is ŝ ₁ =a ₁ , s ₁ , +b ₁ s ₂ + . . . + w ₁ s _(n) ŝ ₂ =a₂ , s ₁ , +b ₂ s ₂ + . . . + w ₂ s _(n) ŝ _(n) =a _(n) , s ₁ , +b _(n) s₂ + . . . + w _(n) s _(n) wherein a₁, a2, . . . , a_(n), b₁, b₂, . . . ,b_(n), w₁, w₂, . . . , w_(n) are constants.
 4. The method according toclaim 3, wherein a₁, a₂, . . . , a_(n), b₁, b₂, . . . b_(n), w₁, w₂, . .. , w_(n) are values of K^(t) ⁻¹ such that a₁, a₂, . . . , a_(n), b₁,b₂, . . . b_(n), w₁, w₂, . . . , w_(n) are equal to K₁₁ ^(t−1), K₁₂^(t−1), . . . , K_(1n) ^(t−1), K₂₁ ^(t−1), K₂₂ ^(t−1), . . . , K_(2n)^(t−1), . . . , K_(n1) ^(t−1), K_(n2) ^(t−1), . . . , K_(nn) ^(t−1),respectively.
 5. The method according to claim 4, wherein K isconstructed via eigenvalue/vector decomposition of N.
 6. The methodaccording to claim 5, wherein when the eigenvalue/vector decompositionof N yields one or more eigenvalues with substantially degenerateeigenvectors, the values of K^(t) ⁻¹ are adjusted such that the outputof the circuit is ŝ=(ŝ ₁, ŝ₂, . . . , ŝ_(m)) where m<n.
 7. The methodaccording to claim 6, wherein substantially all of the image informationin received signals s=(s₁, s₂, . . . , s_(n)) is in output signalsŝ=(ŝ₁, ŝ₂, . . . ,ŝ_(m)).
 8. The method according to claim 6, whereinthe adjustment of the values of K^(t) ⁻¹ results in the received signalswith substantially the same eigenvalues being added together with aphase.
 9. The method according to claim 8, wherein the received signalsare received from quadrature volume coils having fields which aresubstantially uniform and substantially perpendicular, wherein thevalues of K^(t) ⁻¹ are adjusted to accomplish the circularly polarizedaddition of the two received signals, such that substantially all of theimage information in the two received signals is in one output signal.10. The method according to claim 4, further comprising: preamplifyingthe received signals prior to inputting s=(s₁, s₂, . . . , s_(n)) intothe circuit.
 11. The method according to claim 10, further comprising:mixing output signal Ŝ to lower frequencies; sampling Ŝ with a lowerfrequency by A/D converters to produce a digital Ŝ signal; applying a 2DFourier Transform to the digital Ŝ signal; and processing the Ŝ signalafter 2D Fourier Transform applied with image domain matrices to producea plurality of pixel values, Ŝ, for a location, wherein a compositepixel value for the location, {square root}{square root over (Ŝ)}^(t)·Ŝ,utilizes Ŝ after processing with image domain matrices.